Intermediate representation of hyperbolic manifolds by equidistant polyhedra

Abstract

The n-dimensional hyperbolic manifold is usually considered as a homogeneous complex. One compact polytope is su_cient to describe the manifold by pairwise identifying its faces. We discuss an "intermediate" way of representing the manifold by an equidistant (generalized) polyhedron over compact basis as a submanifold of codimension one.